A method of providing session mobility and a user terminal are provided. The method includes, when a session is set through one interface, receiving a request for session transfer to a network corresponding to another interface, checking the available resource capacity of the network to which the session will be transferred, and determining whether or not to transfer the session based on the result of the check operation and establishing a session with the network. The method can improve the reliability of an Internet protocol (IP) multimedia subsystem (IMS) service continuity function.